Related papers: An order-theoretic analysis of interpretations amo…
This paper proposes an alternative to standard first-order logic that seeks greater naturalness, generality, and semantic self-containment. The system removes the first-order restriction, avoids type hierarchies, and dispenses with external…
We consider a family U of finite universes. The second order quantifier Q_R, means for each u in U quantifying over a set of n(R)-place relations isomorphic to a given relation. We define a natural partial order on such quantifiers called…
Tarski gave a general semantics for deductive reasoning: a formula a may be deduced from a set A of formulas iff a holds in all models in which each of the elements of A holds. A more liberal semantics has been considered: a formula a may…
The study of intelligent systems explains behaviour in terms of economic rationality. This results in an optimization principle involving a function or utility, which states that the system will evolve until the configuration of maximum…
Ontologies formalise how the concepts from a given domain are interrelated. Despite their clear potential as a backbone for explainable AI, existing ontologies tend to be highly incomplete, which acts as a significant barrier to their more…
In this paper, we introduce a novel interpreting framework that learns an interpretable model based on an ontology-based sampling technique to explain agnostic prediction models. Different from existing approaches, our algorithm considers…
This paper presents a new system of logic, LF, that is intended to be used as the foundation of the formalization of science. That is, deductive validity according to LF is to be used as the criterion for assessing what follows from the…
Effect systems are lightweight extensions to type systems that can verify a wide range of important properties with modest developer burden. But our general understanding of effect systems is limited primarily to systems where the order of…
The KLM approach to defeasible reasoning introduces a weakened form of implication into classical logic. This allows one to incorporate exceptions to general rules into a logical system, and for old conclusions to be withdrawn upon learning…
Finding a denotational semantics for higher order quantum computation is a long-standing problem in the semantics of quantum programming languages. Most past approaches to this problem fell short in one way or another, either limiting the…
This paper surveys some recent developments towards a dynamic quantum logic and outlines its explicite construction -- some analogies and contrasts with other logics of dynamics are indicated. Abstract: The development of ``(static)…
This paper proposes a formal framework for modeling the interaction of causal and (qualitative) epistemic reasoning. To this purpose, we extend the notion of a causal model with a representation of the epistemic state of an agent. On the…
We are able to derive the equations of motion for forced mechanical systems in a purely variational setting, both in the context of Lagrangian or Hamiltonian mechanics, by duplicating the variables of the system as introduced by Galley…
There exist dozens of interpretations of quantum theory, but they do not seem to contribute much to understanding the theory. This paper attempts to clarify some issues that are discussed in those interpretations. The main keywords are:…
We present a way to apply quantum logic to the study of quantum programs. This is made possible by using an extension of the usual propositional language in order to make transformations performed on the system appear explicitly. This way,…
Protothetic is one of the most stimulating systems for propositional logic. Including quantifiers and an inference rule for definitions, it is a very interesting mean for the study of many questions of metalogic. Unfortunately, it only…
Several different proof translations exist between classical and intuitionistic logic (negative translations), and intuitionistic and linear logic (Girard translations). Our aims in this paper are (1) to consider extensions of…
Quotients and comprehension are fundamental mathematical constructions that can be described via adjunctions in categorical logic. This paper reveals that quotients and comprehension are related to measurement, not only in quantum logic,…
In this paper we present a transformation of finite propositional default theories into so-called propositional argumentation systems. This transformation allows to characterize all notions of Reiter's default logic in the framework of…
Programs with a continuous state space or that interact with physical processes often require notions of equivalence going beyond the standard binary setting in which equivalence either holds or does not hold. In this paper we explore the…